In recent years, according to microminiaturization of patterns for forming semiconductor devices, it is becoming difficult to secure a sufficient margin only by finely adjusting main patterns. Therefore, at present, layout design is performed by using auxiliary patterns (Sub-Resolution Assist Features (SRAFs)) for improving a lithography margin. The SRAFs need to be arranged such that a plurality of process margins can be sufficiently secured. For example, the SRAFs need to be arranged such that process margins such as an exposure amount margin (EL), a depth of focus (DoF: a focus margin), a margin with respect to σ sensitivity of a light source, and a mask enhancement factor (MEF: a mask error sensitivity factor).
As such a method of arranging the SRAFs, there are two kinds of arrangement methods: a rule-base SRAF arranging method and a model-base SRAF arranging method. The rule-base SRAF arranging method is a method in which a lithography designer manually creates, based on budgets of required various process margins, optimum SRAF arrangement rules for each design layout. An optimization degree for the SRAFs is high when the rule-base SRAF arranging method is used. However, there are two disadvantages that long turn around time (TAT) is required for the rule creation and optimization of the SRAFs with respect to a random layout is difficult.
On the other hand, the mode-base SRAF arranging method is a method of carrying out an approximation operation allowable for an exposure device optical system in terms of accuracy to calculate, only from an approximated optical model, optimum SRAF arrangement for improving a certain independent process margin. As the optical mode, a plurality of physical models such as an SRAF arrangement calculation model for maximizing the EL and an SRAF arrangement calculation mode for maximizing the DoF are conceivable. In the model-base SRAF arranging method, there is an advantage that, unlike the rule-base SRAF arranging method, the TAT of SRAF arrangement rule creation is not long and optimum SRAF arrangement can be calculated even with respect to a layout having high randomness.
Outlines of two ideas of the model-base SRAF arranging method are explained below. A first idea is a method of an SRAF arranging technology employing sequential correction. A lithography simulation is performed based on a mask layout in which the SRAFs are arranged. A wafer result w of the mask layout is simulated. The quality of the wafer result w is determined according to process margins of the wafer result w (process window qualification). The SRAF arrangement of the mask layout is sequentially corrected to improve the process margins. In this method, there is an advantage that highly-accurately tuned SRAF arrangement can be performed. However, on the other hand, there is a disadvantage that a calculation amount proportional to the number of times of simulation loop is necessary for the SRAF arrangement and the TAT is extremely long.
A second idea is a method of calculating SRAF arrangement according to a coherence map method. Concerning the coherence map method, for example, United States Patent Application Publication No. 2008/0301620, Japanese Patent No. 3992688, Japanese Patent Application Laid-Open No. 2008-40470, Japanese Patent Application Laid-Open No. 2008-76682, United States Patent Application Publication No. 2004/0229133A1, United States Patent Application Publication No. 2005/0142470A1, United States Patent Application Publication No. 2008/0052334A1, and “R. Socha et al., Proc. SPIE 5377 (2004), pp. 222-pp. 240” are publicly known. In the coherence map method, first, a coherence map is calculated as indicated by the following Formula (I) according to a linear formula of a function w calculated from a circuit pattern, which should be set as a target, and a coherence map kernel Φ:Ψ=wΦ  (1)
where,  indicates convolutional integration operation.
Subsequently, SRAFs “m” from which SRAFs considered optimum can be manufactured as a mask are extracted based on the calculated coherence map Ψ. As an extraction method, SRAFs that are present in an area including a mask area defined by the following Formula (2) and include mask constraints (e.g., constraints for a mask layout for making it easy to set, in manufacturing, the size and the position in a rectilinear polygon including vertical and horizontal segments) are extracted:M={(x,y)|Ψ(x,y)>Threshold}  (2)
where, “Threshold” is an optimum positive number.
An advantage of the coherence map method is the shortness of the TAT. However, because of the principle of the coherence map method that the approximation calculation is performed, there is a problem in SRAF arrangement accuracy. Specifically, first, in the present coherence map mode, a coherence map kernel Ψ subjected to approximation calculation taking into account only improvement of one process margin is used. SRAFs having high robustness against the other process margins not taken into account cannot be generated. As an example, in a model using the coherence map kernel Φ subjected to the approximation calculation taking into account only improvement of the exposure amount margin, SRAFs having high robustness against the process margins other than the exposure amount margin cannot be generated. Therefore, the SRAFs are not SRAFs optimized for patterns actually arranged on an LSI. Further, in a process of polygonization for generating SRAFs from the coherence map Φ, deterioration in accuracy with respect to a degree of process margin improvement occurs depending on a type of a mask layout.